Decorrelation-Based Feature Discovery: DARWIN-Whole
Jose Tamez
2024-01-04
- 1 Effect of UPSTM-Based Decorrelation
on Feature Discovery
- 1.0.1 Loading the libraries
- 1.1 Material and Methods
- 1.2 The Data
- 1.3 Generaring the report
- 1.4 The heatmap of the data
- 1.5 The decorrelation
- 1.6 The heatmap of the decorrelated data
- 1.7 The correlation matrix after decorrelation
- 1.8 U-MAP Visualization of features
- 1.9 Univariate Analysis
- 1.10 Comparing ILAA vs PCA vs EFA
- 1.11 Effect on CAR modeling
1 Effect of UPSTM-Based Decorrelation on Feature Discovery
1.0.1 Loading the libraries
library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)
op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)1.1 Material and Methods
1.2 The Data
DARWIN <- read.csv("~/GitHub/FCA/Data/DARWIN/DARWIN.csv")
rownames(DARWIN) <- DARWIN$ID
DARWIN$ID <- NULL
DARWIN$class <- 1*(DARWIN$class=="P")
print(table(DARWIN$class))
#>
#> 0 1
#> 85 89
DARWIN[,1:ncol(DARWIN)] <- sapply(DARWIN,as.numeric)
signedlog <- function(x) { return (sign(x)*log(abs(1.0e12*x)+1.0))}
whof <- !(colnames(DARWIN) %in% c("class"));
DARWIN[,whof] <- signedlog(DARWIN[,whof])
1.2.0.1 Standarize the names for the reporting
studyName <- "DARWIN"
dataframe <- DARWIN
outcome <- "class"
TopVariables <- 10
thro <- 0.80
cexheat = 0.151.3 Generaring the report
1.3.1 Libraries
Some libraries
library(psych)
library(whitening)
library("vioplot")
library("rpart")1.3.2 Data specs
pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))| rows | col |
|---|---|
| 174 | 450 |
pander::pander(table(dataframe[,outcome]))| 0 | 1 |
|---|---|
| 85 | 89 |
varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]
largeSet <- length(varlist) > 1500 1.3.3 Scaling the data
Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns
### Some global cleaning
sdiszero <- apply(dataframe,2,sd) > 1.0e-16
dataframe <- dataframe[,sdiszero]
varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
dataframe <- dataframe[,tokeep]
varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]
iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples
dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData1.4 The heatmap of the data
numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000
if (!largeSet)
{
hm <- heatMaps(data=dataframeScaled[1:numsub,],
Outcome=outcome,
Scale=TRUE,
hCluster = "row",
xlab="Feature",
ylab="Sample",
srtCol=45,
srtRow=45,
cexCol=cexheat,
cexRow=cexheat
)
par(op)
}
1.4.0.1 Correlation Matrix of the Data
The heat map of the data
if (!largeSet)
{
par(cex=0.6,cex.main=0.85,cex.axis=0.7)
#cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
cormat <- cor(dataframe[,varlist],method="pearson")
cormat[is.na(cormat)] <- 0
gplots::heatmap.2(abs(cormat),
trace = "none",
# scale = "row",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Original Correlation",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Pearson Correlation|",
xlab="Feature", ylab="Feature")
diag(cormat) <- 0
print(max(abs(cormat)))
}
[1]
0.9994118
1.5 The decorrelation
DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#>
#> gmrt_on_paper5 mean_jerk_on_paper14 mean_jerk_on_paper16 gmrt_on_paper18 mean_jerk_on_paper3 mean_acc_in_air25
#> air_time1 disp_index1 gmrt_in_air1 gmrt_on_paper1
#> 0.43777778 0.48222222 0.49111111 0.79333333
#> max_x_extension1 max_y_extension1
#> 0.02222222 0.15111111
#>
#> Included: 450 , Uni p: 0.0003333333 , Base Size: 21 , Rcrit: 0.2555213
#>
#>
1 <R=0.945,thr=0.950>, Top: 75< 9 >[Fa= 75 ]( 75 , 131 , 0 ),<|><>Tot Used: 206 , Added: 131 , Zero Std: 0 , Max Cor: 0.990
#>
2 <R=0.893,thr=0.950>, Top: 5< 3 >[Fa= 80 ]( 5 , 7 , 75 ),<|><>Tot Used: 212 , Added: 7 , Zero Std: 0 , Max Cor: 0.950
#>
3 <R=0.888,thr=0.900>, Top: 39< 1 >[Fa= 104 ]( 37 , 39 , 80 ),<|><>Tot Used: 260 , Added: 39 , Zero Std: 0 , Max Cor: 0.919
#>
4 <R=0.862,thr=0.900>, Top: 3< 1 >[Fa= 104 ]( 3 , 3 , 104 ),<|><>Tot Used: 260 , Added: 3 , Zero Std: 0 , Max Cor: 0.899
#>
5 <R=0.860,thr=0.800>, Top: 50< 1 >[Fa= 135 ]( 48 , 60 , 104 ),<|><>Tot Used: 327 , Added: 60 , Zero Std: 0 , Max Cor: 0.874
#>
6 <R=0.837,thr=0.800>, Top: 12< 1 >[Fa= 144 ]( 12 , 12 , 135 ),<|><>Tot Used: 336 , Added: 12 , Zero Std: 0 , Max Cor: 0.926
#>
7 <R=0.880,thr=0.900>, Top: 1< 1 >[Fa= 144 ]( 1 , 1 , 144 ),<|><>Tot Used: 336 , Added: 1 , Zero Std: 0 , Max Cor: 0.887
#>
8 <R=0.869,thr=0.800>, Top: 2< 1 >[Fa= 144 ]( 2 , 2 , 144 ),<|><>Tot Used: 336 , Added: 2 , Zero Std: 0 , Max Cor: 0.799
#>
9 <R=0.799,thr=0.800>
#>
[ 9 ], 0.79919 Decor Dimension: 336 Nused: 336 . Cor to Base: 209 , ABase: 450 , Outcome Base: 0
#>
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]
pander::pander(sum(apply(dataframe[,varlist],2,var)))692
pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))135
pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))4.57
pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))4.45
varratio <- attr(DEdataframe,"VarRatio")
pander::pander(tail(varratio))| La_mean_acc_on_paper14 | La_max_x_extension5 | La_mean_jerk_in_air25 | La_mean_jerk_in_air17 | La_mean_speed_on_paper5 | La_mean_speed_on_paper12 |
|---|---|---|---|---|---|
| 0.00256 | 0.00219 | 0.00218 | 0.00133 | 0.00118 | 0.000866 |
1.5.1 The decorrelation matrix
if (!largeSet)
{
par(cex=0.6,cex.main=0.85,cex.axis=0.7)
UPLTM <- attr(DEdataframe,"UPLTM")
gplots::heatmap.2(1.0*(abs(UPLTM)>0),
trace = "none",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Decorrelation matrix",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Beta|>0",
xlab="Output Feature", ylab="Input Feature")
par(op)
}
1.5.2 Formulas Network
Displaying the features associations
par(op)
clustable <- c("To many variables")
transform <- attr(DEdataframe,"UPLTM") != 0
tnames <- colnames(transform)
colnames(transform) <- str_remove_all(colnames(transform),"La_")
transform <- abs(transform*cor(dataframe[,rownames(transform)])) # The weights are proportional to the observed correlation
fscore <- attr(DEdataframe,"fscore")
VertexSize <- fscore # The size depends on the variable independence relevance (fscore)
names(VertexSize) <- str_remove_all(names(VertexSize),"La_")
VertexSize <- 10*(VertexSize-min(VertexSize))/(max(VertexSize)-min(VertexSize)) # Normalization
VertexSize <- VertexSize[rownames(transform)]
rsum <- apply(1*(transform !=0),1,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
csum <- apply(1*(transform !=0),2,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
ntop <- min(10,length(rsum))
topfeatures <- unique(c(names(rsum[order(-rsum)])[1:ntop],names(csum[order(-csum)])[1:ntop]))
rtrans <- transform[topfeatures,]
csum <- (apply(1*(rtrans !=0),2,sum) > 1*(colnames(rtrans) %in% topfeatures))
rtrans <- rtrans[,csum]
topfeatures <- unique(c(topfeatures,colnames(rtrans)))
print(ncol(transform))[1] 336
transform <- transform[topfeatures,topfeatures]
print(ncol(transform))[1] 90
if (ncol(transform)>100)
{
csum <- apply(1*(transform !=0),1,sum)
csum <- csum[csum > 1]
csum <- csum + 0.01*VertexSize[names(csum)]
csum <- csum[order(-csum)]
tpsum <- min(20,length(csum))
trsum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
rtrans <- transform[trsum,]
topfeatures <- unique(c(rownames(rtrans),colnames(rtrans)))
transform <- transform[topfeatures,topfeatures]
if (nrow(transform) > 150)
{
csum <- apply(1*(rtrans != 0 ),2,sum)
csum <- csum + 0.01*VertexSize[names(csum)]
csum <- csum[order(-csum)]
tpsum <- min(130,length(csum))
csum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
csum <- unique(c(trsum,csum))
transform <- transform[csum,csum]
}
print(ncol(transform))
}
if (ncol(transform) < 150)
{
gplots::heatmap.2(transform,
trace = "none",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Red Decorrelation matrix",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Beta|>0",
xlab="Output Feature", ylab="Input Feature")
par(op)
VertexSize <- VertexSize[colnames(transform)]
gr <- graph_from_adjacency_matrix(transform,mode = "directed",diag = FALSE,weighted=TRUE)
gr$layout <- layout_with_fr
# fc <- cluster_optimal(gr)
fc <- cluster_walktrap (gr,steps=50)
plot(fc, gr,
edge.width = 2*E(gr)$weight,
vertex.size=VertexSize,
edge.arrow.size=0.5,
edge.arrow.width=0.5,
vertex.label.cex=(0.15+0.05*VertexSize),
vertex.label.dist=0.5 + 0.05*VertexSize,
main="Top Feature Association")
varratios <- varratio
fscores <- fscore
names(varratios) <- str_remove_all(names(varratios),"La_")
names(fscores) <- str_remove_all(names(fscores),"La_")
dc <- getLatentCoefficients(DEdataframe)
theCharformulas <- attr(dc,"LatentCharFormulas")
clustable <- as.data.frame(cbind(Variable=fc$names,
Formula=as.character(theCharformulas[paste("La_",fc$names,sep="")]),
Class=fc$membership,
ResidualVariance=round(varratios[fc$names],3),
Fscore=round(fscores[fc$names],3)
)
)
rownames(clustable) <- str_replace_all(rownames(clustable),"__","_")
clustable$Variable <- NULL
clustable$Class <- as.integer(clustable$Class)
clustable$ResidualVariance <- as.numeric(clustable$ResidualVariance)
clustable$Fscore <- as.numeric(clustable$Fscore)
clustable <- clustable[order(-clustable$Fscore),]
clustable <- clustable[order(clustable$Class),]
clustable <- clustable[clustable$Fscore >= -1,]
topv <- min(50,nrow(clustable))
clustable <- clustable[1:topv,]
}
pander::pander(clustable)| Formula | Class | ResidualVariance | Fscore | |
|---|---|---|---|---|
| gmrt_on_paper12 | NA | 1 | 1.000 | 7 |
| paper_time12 | - (1.034)gmrt_on_paper12 + paper_time12 | 1 | 0.115 | 5 |
| mean_acc_on_paper12 | - (0.768)gmrt_on_paper12 + mean_acc_on_paper12 | 1 | 0.033 | 0 |
| disp_index12 | + disp_index12 - (0.438)paper_time12 | 1 | 0.019 | -1 |
| max_x_extension12 | - (1.034)gmrt_on_paper12 + max_x_extension12 | 1 | 0.032 | -1 |
| num_of_pendown12 | + num_of_pendown12 - (0.795)paper_time12 | 1 | 0.084 | -1 |
| pressure_var12 | - (1.064)paper_time12 + pressure_var12 | 1 | 0.085 | -1 |
| gmrt_on_paper18 | NA | 2 | 1.000 | 9 |
| disp_index18 | + disp_index18 - (0.452)gmrt_on_paper18 | 2 | 0.101 | 3 |
| mean_jerk_on_paper18 | - (0.707)gmrt_on_paper18 + mean_jerk_on_paper18 | 2 | 0.020 | 0 |
| mean_speed_on_paper18 | - (0.882)gmrt_on_paper18 + mean_speed_on_paper18 | 2 | 0.004 | -1 |
| pressure_mean18 | - (1.044)gmrt_on_paper18 + pressure_mean18 | 2 | 0.026 | -1 |
| pressure_var18 | - (1.161)gmrt_on_paper18 + pressure_var18 | 2 | 0.083 | -1 |
| mean_jerk_on_paper3 | NA | 3 | 1.000 | 10 |
| gmrt_on_paper3 | + gmrt_on_paper3 - (1.382)mean_jerk_on_paper3 | 3 | 0.033 | 1 |
| paper_time3 | - (1.561)mean_jerk_on_paper3 + paper_time3 | 3 | 0.022 | 0 |
| max_x_extension3 | + max_x_extension3 - (1.537)mean_jerk_on_paper3 | 3 | 0.023 | -1 |
| max_y_extension3 | + max_y_extension3 - (1.448)mean_jerk_on_paper3 | 3 | 0.055 | -1 |
| mean_acc_on_paper3 | + mean_acc_on_paper3 - (1.092)mean_jerk_on_paper3 | 3 | 0.004 | -1 |
| num_of_pendown3 | - (1.221)mean_jerk_on_paper3 + num_of_pendown3 | 3 | 0.047 | -1 |
| pressure_mean3 | - (1.501)mean_jerk_on_paper3 + pressure_mean3 | 3 | 0.011 | -1 |
| pressure_var3 | - (1.672)mean_jerk_on_paper3 + pressure_var3 | 3 | 0.035 | -1 |
| mean_jerk_on_paper16 | NA | 4 | 1.000 | 10 |
| gmrt_on_paper16 | + gmrt_on_paper16 - (1.376)mean_jerk_on_paper16 | 4 | 0.032 | 0 |
| max_y_extension16 | + max_y_extension16 - (1.494)mean_jerk_on_paper16 | 4 | 0.037 | 0 |
| paper_time16 | - (1.484)mean_jerk_on_paper16 + paper_time16 | 4 | 0.068 | 0 |
| mean_acc_on_paper16 | + mean_acc_on_paper16 - (1.089)mean_jerk_on_paper16 | 4 | 0.004 | -1 |
| num_of_pendown16 | - (1.227)mean_jerk_on_paper16 + num_of_pendown16 | 4 | 0.082 | -1 |
| pressure_mean16 | - (1.467)mean_jerk_on_paper16 + pressure_mean16 | 4 | 0.024 | -1 |
| pressure_var16 | - (1.670)mean_jerk_on_paper16 + pressure_var16 | 4 | 0.054 | -1 |
| mean_jerk_on_paper2 | NA | 5 | 1.000 | 10 |
| gmrt_on_paper2 | + gmrt_on_paper2 - (1.369)mean_jerk_on_paper2 | 5 | 0.058 | 0 |
| max_y_extension2 | + max_y_extension2 - (1.544)mean_jerk_on_paper2 | 5 | 0.021 | 0 |
| paper_time2 | - (1.572)mean_jerk_on_paper2 + paper_time2 | 5 | 0.043 | 0 |
| max_x_extension2 | + max_x_extension2 - (1.465)mean_jerk_on_paper2 | 5 | 0.071 | -1 |
| mean_acc_on_paper2 | + mean_acc_on_paper2 - (1.092)mean_jerk_on_paper2 | 5 | 0.008 | -1 |
| num_of_pendown2 | - (1.250)mean_jerk_on_paper2 + num_of_pendown2 | 5 | 0.105 | -1 |
| pressure_var2 | - (1.684)mean_jerk_on_paper2 + pressure_var2 | 5 | 0.066 | -1 |
| mean_speed_on_paper21 | NA | 6 | 1.000 | 4 |
| mean_acc_on_paper21 | + mean_acc_on_paper21 + (0.602)mean_speed_on_paper21 | 6 | 0.297 | 0 |
| paper_time21 | + (0.912)mean_speed_on_paper21 + paper_time21 | 6 | 0.347 | 0 |
| disp_index21 | + disp_index21 - (0.855)mean_speed_on_paper21 - (0.937)paper_time21 | 6 | 0.275 | -1 |
| gmrt_on_paper21 | + gmrt_on_paper21 - (0.939)mean_speed_on_paper21 | 6 | 0.055 | -1 |
| total_time21 | + (1.007)mean_speed_on_paper21 + total_time21 | 6 | 0.263 | -1 |
| mean_jerk_on_paper14 | NA | 7 | 1.000 | 10 |
| gmrt_on_paper14 | + gmrt_on_paper14 - (1.391)mean_jerk_on_paper14 | 7 | 0.020 | 0 |
| paper_time14 | - (1.527)mean_jerk_on_paper14 + paper_time14 | 7 | 0.036 | 0 |
| max_x_extension14 | + max_x_extension14 - (1.506)mean_jerk_on_paper14 | 7 | 0.051 | -1 |
| max_y_extension14 | + max_y_extension14 - (1.526)mean_jerk_on_paper14 | 7 | 0.040 | -1 |
| mean_acc_on_paper14 | + mean_acc_on_paper14 - (1.091)mean_jerk_on_paper14 | 7 | 0.003 | -1 |
par(op)
1.6 The heatmap of the decorrelated data
if (!largeSet)
{
hm <- heatMaps(data=DEdataframe[1:numsub,],
Outcome=outcome,
Scale=TRUE,
hCluster = "row",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
xlab="Feature",
ylab="Sample")
par(op)
}
1.7 The correlation matrix after decorrelation
if (!largeSet)
{
cormat <- cor(DEdataframe[,varlistc],method="pearson")
cormat[is.na(cormat)] <- 0
gplots::heatmap.2(abs(cormat),
trace = "none",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Correlation after ILAA",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Pearson Correlation|",
xlab="Feature", ylab="Feature")
par(op)
diag(cormat) <- 0
print(max(abs(cormat)))
}
[1]
0.79919
1.8 U-MAP Visualization of features
1.8.1 The UMAP on Raw Data
classes <- unique(dataframe[1:numsub,outcome])
raincolors <- rainbow(length(classes))
names(raincolors) <- classes
topvars <- univariate_BinEnsemble(dataframe,outcome)
lso <- LASSO_MIN(formula(paste(outcome,"~.")),dataframe,family="binomial")
topvars <- unique(c(names(topvars),lso$selectedfeatures))
pander::pander(head(topvars))air_time17, total_time17, air_time23, total_time23, air_time7 and total_time15
# names(topvars)
#if (nrow(dataframe) < 1000)
#{
datasetframe.umap = umap(scale(dataframe[1:numsub,topvars]),n_components=2)
# datasetframe.umap = umap(dataframe[1:numsub,varlist],n_components=2)
plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])
#}1.8.2 The decorralted UMAP
varlistcV <- names(varratio[varratio >= 0.01])
topvars <- univariate_BinEnsemble(DEdataframe[,varlistcV],outcome)
lso <- LASSO_MIN(formula(paste(outcome,"~.")),DEdataframe[,varlistcV],family="binomial")
topvars <- unique(c(names(topvars),lso$selectedfeatures))
pander::pander(head(topvars))air_time17, total_time23, total_time15, total_time6, total_time7 and mean_acc_in_air17
varlistcV <- varlistcV[varlistcV != outcome]
# DEdataframe[,outcome] <- as.numeric(DEdataframe[,outcome])
#if (nrow(dataframe) < 1000)
#{
datasetframe.umap = umap(scale(DEdataframe[1:numsub,topvars]),n_components=2)
# datasetframe.umap = umap(DEdataframe[1:numsub,varlistcV],n_components=2)
plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After ILAA",t='n')
text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])
#}1.9 Univariate Analysis
1.9.1 Univariate
univarRAW <- uniRankVar(varlist,
paste(outcome,"~1"),
outcome,
dataframe,
rankingTest="AUC")100 : mean_jerk_in_air6 200 : disp_index12 300 : mean_speed_in_air17 400 : gmrt_on_paper23
univarDe <- uniRankVar(varlistc,
paste(outcome,"~1"),
outcome,
DEdataframe,
rankingTest="AUC",
)100 : La_mean_jerk_in_air6 200 : La_disp_index12 300 : La_mean_speed_in_air17 400 : La_gmrt_on_paper23
1.9.2 Final Table
univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")
##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)| caseMean | caseStd | controlMean | controlStd | controlKSP | ROCAUC | |
|---|---|---|---|---|---|---|
| total_time23 | 37.2 | 0.503 | 36.7 | 0.484 | 1.03e-05 | 0.863 |
| total_time15 | 38.1 | 0.875 | 37.1 | 0.421 | 5.44e-01 | 0.844 |
| air_time23 | 36.6 | 0.626 | 35.9 | 0.656 | 6.92e-03 | 0.844 |
| air_time15 | 37.7 | 1.094 | 36.6 | 0.615 | 5.06e-01 | 0.829 |
| total_time17 | 38.5 | 0.681 | 37.8 | 0.614 | 4.00e-03 | 0.824 |
| paper_time23 | 36.4 | 0.439 | 36.0 | 0.231 | 6.72e-01 | 0.814 |
| air_time17 | 37.9 | 0.914 | 37.0 | 0.795 | 3.52e-02 | 0.806 |
| paper_time17 | 37.6 | 0.395 | 37.2 | 0.439 | 1.28e-03 | 0.796 |
| total_time6 | 37.1 | 0.777 | 36.4 | 0.447 | 7.16e-01 | 0.790 |
| air_time16 | 36.4 | 1.131 | 35.2 | 0.867 | 9.38e-01 | 0.787 |
topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]
pander::pander(finalTable)| caseMean | caseStd | controlMean | controlStd | controlKSP | ROCAUC | |
|---|---|---|---|---|---|---|
| total_time23 | 37.2307 | 0.503 | 36.666 | 0.484 | 1.03e-05 | 0.863 |
| total_time15 | 38.0918 | 0.875 | 37.146 | 0.421 | 5.44e-01 | 0.844 |
| air_time17 | 37.9116 | 0.914 | 37.000 | 0.795 | 3.52e-02 | 0.806 |
| paper_time17 | 37.6037 | 0.395 | 37.205 | 0.439 | 1.28e-03 | 0.796 |
| total_time6 | 37.1004 | 0.777 | 36.368 | 0.447 | 7.16e-01 | 0.790 |
| air_time16 | 36.3573 | 1.131 | 35.240 | 0.867 | 9.38e-01 | 0.787 |
| total_time7 | 37.1660 | 0.690 | 36.578 | 0.812 | 1.87e-03 | 0.785 |
| total_time22 | 37.2925 | 0.783 | 36.656 | 0.346 | 5.74e-01 | 0.780 |
| gmrt_in_air7 | 32.9484 | 0.405 | 33.382 | 0.396 | 9.99e-01 | 0.775 |
| total_time9 | 37.0580 | 0.769 | 36.334 | 0.482 | 7.12e-01 | 0.774 |
| La_pressure_var5 | 1.2955 | 1.270 | 0.409 | 0.837 | 4.47e-01 | 0.738 |
| La_pressure_mean2 | 0.0214 | 0.298 | 0.219 | 0.156 | 7.30e-02 | 0.737 |
| La_disp_index17 | -35.4440 | 0.142 | -35.557 | 0.134 | 1.61e-01 | 0.731 |
| La_gmrt_on_paper2 | 0.3429 | 0.605 | 0.821 | 0.488 | 7.04e-01 | 0.725 |
| La_paper_time23 | 57.6825 | 0.224 | 57.508 | 0.204 | 8.41e-01 | 0.723 |
dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")
pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))| mean | total | fraction |
|---|---|---|
| 2.17 | 221 | 0.491 |
theCharformulas <- attr(dc,"LatentCharFormulas")
topvar <- rownames(tableRaw)
finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])
orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]
finalTable$varratio <- varratio[rownames(finalTable)]
Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores","varratio")
finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])| DecorFormula | caseMean | caseStd | controlMean | controlStd | controlKSP | ROCAUC | RAWAUC | fscores | varratio | |
|---|---|---|---|---|---|---|---|---|---|---|
| total_time23 | NA | 37.2307 | 0.503 | 36.666 | 0.484 | 1.03e-05 | 0.863 | 0.863 | 1 | 1.00000 |
| total_time15 | NA | 38.0918 | 0.875 | 37.146 | 0.421 | 5.44e-01 | 0.844 | 0.844 | 1 | 1.00000 |
| air_time23 | NA | 36.6116 | 0.626 | 35.858 | 0.656 | 6.92e-03 | 0.844 | 0.844 | NA | NA |
| air_time15 | NA | 37.7203 | 1.094 | 36.607 | 0.615 | 5.06e-01 | 0.829 | 0.829 | NA | NA |
| total_time17 | NA | 38.5262 | 0.681 | 37.848 | 0.614 | 4.00e-03 | 0.824 | 0.824 | NA | NA |
| paper_time23 | NA | 36.4011 | 0.439 | 36.001 | 0.231 | 6.72e-01 | 0.814 | 0.814 | NA | NA |
| air_time17 | NA | 37.9116 | 0.914 | 37.000 | 0.795 | 3.52e-02 | 0.806 | 0.806 | 1 | 1.00000 |
| paper_time17 | NA | 37.6037 | 0.395 | 37.205 | 0.439 | 1.28e-03 | 0.796 | 0.796 | 0 | 1.00000 |
| total_time6 | NA | 37.1004 | 0.777 | 36.368 | 0.447 | 7.16e-01 | 0.790 | 0.790 | 1 | 1.00000 |
| air_time16 | NA | 36.3573 | 1.131 | 35.240 | 0.867 | 9.38e-01 | 0.787 | 0.787 | 1 | 1.00000 |
| total_time7 | NA | 37.1660 | 0.690 | 36.578 | 0.812 | 1.87e-03 | 0.785 | 0.785 | 1 | 1.00000 |
| total_time22 | NA | 37.2925 | 0.783 | 36.656 | 0.346 | 5.74e-01 | 0.780 | 0.780 | 1 | 1.00000 |
| gmrt_in_air7 | NA | 32.9484 | 0.405 | 33.382 | 0.396 | 9.99e-01 | 0.775 | 0.775 | 1 | 1.00000 |
| total_time9 | NA | 37.0580 | 0.769 | 36.334 | 0.482 | 7.12e-01 | 0.774 | 0.774 | 2 | 1.00000 |
| La_pressure_var5 | - (1.169)gmrt_on_paper5 + pressure_var5 | 1.2955 | 1.270 | 0.409 | 0.837 | 4.47e-01 | 0.738 | 0.274 | -1 | 0.07763 |
| La_pressure_mean2 | - (0.970)max_y_extension2 + (3.71e-03)mean_jerk_on_paper2 + pressure_mean2 | 0.0214 | 0.298 | 0.219 | 0.156 | 7.30e-02 | 0.737 | 0.312 | -2 | 0.00938 |
| La_disp_index17 | + disp_index17 - (1.415)max_y_extension17 | -35.4440 | 0.142 | -35.557 | 0.134 | 1.61e-01 | 0.731 | 0.736 | -1 | 0.26605 |
| La_gmrt_on_paper2 | + gmrt_on_paper2 - (1.369)mean_jerk_on_paper2 | 0.3429 | 0.605 | 0.821 | 0.488 | 7.04e-01 | 0.725 | 0.337 | 0 | 0.05839 |
| La_paper_time23 | + (0.746)mean_speed_on_paper23 + paper_time23 | 57.6825 | 0.224 | 57.508 | 0.204 | 8.41e-01 | 0.723 | 0.814 | 0 | 0.32434 |
1.10 Comparing ILAA vs PCA vs EFA
1.10.1 PCA
featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE,tol=0.01) #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous])
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)
#pander::pander(pc$rotation)
PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])
gplots::heatmap.2(abs(PCACor),
trace = "none",
# scale = "row",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "PCA Correlation",
cexRow = 0.5,
cexCol = 0.5,
srtCol=45,
srtRow= -45,
key.title=NA,
key.xlab="Pearson Correlation",
xlab="Feature", ylab="Feature")
1.10.2 EFA
EFAdataframe <- dataframeScaled
if (length(iscontinous) < 2000)
{
topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)-1)
if (topred < 2) topred <- 2
uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE) # EFA analysis
predEFA <- predict(uls,dataframeScaled[,iscontinous])
EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous])
EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
gplots::heatmap.2(abs(EFACor),
trace = "none",
# scale = "row",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "EFA Correlation",
cexRow = 0.5,
cexCol = 0.5,
srtCol=45,
srtRow= -45,
key.title=NA,
key.xlab="Pearson Correlation",
xlab="Feature", ylab="Feature")
}
1.11 Effect on CAR modeling
par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(rawmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
}
pander::pander(table(dataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 78 | 7 |
| 1 | 7 | 82 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.920 | 0.869 | 0.955 |
| 3 | se | 0.921 | 0.845 | 0.968 |
| 4 | sp | 0.918 | 0.838 | 0.966 |
| 6 | diag.or | 130.531 | 43.775 | 389.223 |
par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe[,c(outcome,varlistcV)],control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(IDeAmodel,main="ILAA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(IDeAmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
}
pander::pander(table(DEdataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 74 | 11 |
| 1 | 5 | 84 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.908 | 0.855 | 0.947 |
| 3 | se | 0.944 | 0.874 | 0.982 |
| 4 | sp | 0.871 | 0.780 | 0.934 |
| 6 | diag.or | 113.018 | 37.532 | 340.322 |
par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(PCAmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}
pander::pander(table(PCAdataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 65 | 20 |
| 1 | 2 | 87 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.874 | 0.815 | 0.919 |
| 3 | se | 0.978 | 0.921 | 0.997 |
| 4 | sp | 0.765 | 0.660 | 0.850 |
| 6 | diag.or | 141.375 | 31.905 | 626.443 |
par(op)1.11.1 EFA
EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(EFAmodel,EFAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(EFAmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
}
pander::pander(table(EFAdataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 80 | 5 |
| 1 | 33 | 56 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.782 | 0.713 | 0.841 |
| 3 | se | 0.629 | 0.520 | 0.729 |
| 4 | sp | 0.941 | 0.868 | 0.981 |
| 6 | diag.or | 27.152 | 9.982 | 73.854 |
par(op)